Define knots (and links), discuss wild and tame knots, state that we restrict to the latter ones, introduce (ambient) isotopies, knot equivalences (leave out delta moves if you need to save time), knot projections, Reidemeister moves and discuss the characterisation of knot equivalences in terms of Reidemeister moves. (Burde-Zieschang, Chapter 1.A-C).

Define Mirror images, invertible and amphicheiral knots, alternating knot projections, Seifert surfaces and genus, meridian and longitude, knot sums (sometimes called products), companion and satellite knots and discuss tricolorability as an elementary invariant of knots. (Burde-Zieschang, Chapter 2.A-C and Adams, Chapter 1.5 for tricolorability).

Discuss the homology of the knot complement, the Wirtinger Presentation of the knot group, define companion and satellite knots and discuss the knot groups of satellite and companion knots. (Burde-Zieschang, Def. 2.8 and Chapter 3.A and 3.B).

Discuss peripheral systems, Waldhausen's Theorem and the characterisation of invertibility and amphicheirality. Finally, show the asphericity of the knot complement. (Burde-Zieschang, Chapter 3.C and 3.F).

Discuss cyclic knot coverings and the Alexander module, band projections, Seifert matrices, Alexander matrices, Alexander polynomials and their properties. (Burde-Zieschang, Chapter 8.A-D.

Discuss the homology of covering spaces, Fox differential calculus and the calculation of Alexander matrices and polynomials. (Burde-Zieschang, Chapter 9.A-C)

Introduce quandles, abelian quandles, conjugation quandles, Alexander quandles, involutary quandles (Kei), the core, homomorphisms of quandles, free quandles, show that free quandles arise as subquandles of free groups, discuss admissible equivalence relations, presentations of quandles and the adjunction. Stress the non-injectivity of the unit of the adjunction. (Joyce, Sections 1 and 2.1 and Nardin for Alexander quandles, free quandles, admissible equivalence relations and presentations.)

Define coset quandles and homogeneous quandles and show that the latter are coset quandles. State the generalization to general quandles and discuss augmented quandles, their homomorphisms, limits and colimits and finally, their quotients arising from normal subgroups. (Joyce, Sections 2.4, 2.10 and 2.11).

Introduce the fundamental quandle of a pair of spaces. Instead of copying the uninformative formulas, draw informative pictures (of nooses, the action of loops on nooses,...). Follow the formal viewpoint as you find suitable. Show that the fundamental quandle of a disk with respect to the center point gives essentially the winding number. (Joyce, Sections 4.1 and 4.2)

Show the Seifert--van Kampen theorem for quandles. To do so, it might be helpful to recall the categorical concept of a pushout and van Kampen's theorem for fundamental groups of spaces with open covers. As examples, consider punctured surfaces. (Joyce, Sections 4.3 and 4.4).

Give the geometric defintion of a knot quandle as the subquandle of the fundamental quandle of nooses with winding number one. Explain how to obtain a knot quandle from a Wirtinger presentation of the knot group. Explain briefly that the latter is a knot invariant using Reidemeister moves. Using van Kampen's theorem, show that the two definitions give isomorphic quandles. (Joyce, Sections 4.5-4.8).

Show that the knot quandle is a complete knot invariant by showing that it encodes the peripheral subgroup structure. Show that the Alexander invariant and the abelian knot quandle determine each other. If time permits, mention cyclic knot invariants and involutory knot quandles. (Joyce, Sections 4.9-4.12).